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Simplifying 5z2 + 20z + 40 = 0 Reorder the terms: 40 + 20z + 5z2 = 0 Solving 40 + 20z + 5z2 = 0 Solving for variable 'z'. Factor out the Greatest Common Factor (GCF), '5'. 5(8 + 4z + z2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(8 + 4z + z2)' equal to zero and attempt to solve: Simplifying 8 + 4z + z2 = 0 Solving 8 + 4z + z2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 4z + -8 + z2 = 0 + -8 Reorder the terms: 8 + -8 + 4z + z2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 4z + z2 = 0 + -8 4z + z2 = 0 + -8 Combine like terms: 0 + -8 = -8 4z + z2 = -8 The z term is 4z. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4z + 4 + z2 = -8 + 4 Reorder the terms: 4 + 4z + z2 = -8 + 4 Combine like terms: -8 + 4 = -4 4 + 4z + z2 = -4 Factor a perfect square on the left side: (z + 2)(z + 2) = -4 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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